Sharing Lightroom images in DNG with ability to undo/redo edits in another application?

Are there any applications other than Lightroom in which I can undo/redo Lightroom edits if I already have the DNG?

No. Each raw processing application is proprietary. Each application uses different algorithms for each camera that it can handle raw files from than other applications use for files from the same camera. Instructions appended to a raw file in one application, such as the instructions created by your client of how to process the DNG file using LR, are not usable by other raw processing applications and vice versa.

If you open the DNGs in any application other than Lightroom (or any other Adobe products, such as Photoshop, that also use Adobe Camera Raw under the hood as LR does) you will not be able to apply, roll back, or reapply edits made using LR. At best you might initially see the converted results of those edits in a JPEG preview image that is not an actual part of the editable raw image data but is only one among near countless possible legitimate interpretations of the raw data. Preview JPEGs are embedded so they can be quickly displayed without having to wait to process the actual raw information in the raw image file. If it hasn't already switched over to its own interpretation, once you actually start doing any editing adjustments using the actual raw data, your application will stop displaying the preview image and begin to display its own conversion of the actual raw image data in the file based on your instructions.

If I choose to edit the DNG in a non-Adobe application such as Luminar / Dark Table or another, e.g. Shotkit, then will the DNG images open as if the photographer had made no edits (i.e. in RAW original) or would they open with the edits applied?

First, a little about what a raw file is and what it is not.

There's no such thing as a "RAW original". There are only a near countless possible interpretations of the raw image data.

Anytime you open a raw file and look at it on your screen, you are not viewing "THE raw file." ¹ You are viewing one among a near-countless number of possible interpretations of the data in the raw file. The raw data itself contains a single (monochrome) linear brightness value measured by each pixel well. With Bayer masked camera sensors (the vast majority of color digital cameras use Bayer filters) each pixel well has a color filter in front of it that is either 'red', 'green', or 'blue'. (The actual 'colors' of the filters in most Bayer Masks are anywhere from a slightly yellowish-green to an orange-yellow for 'red", a slightly bluish-green for 'green' and a slightly bluish-violet for 'blue' - these colors more or less correspond to the center of sensitivity for the three types of cones in our retinas. They do not correspond to the colors our emissive displays use for 'red', 'green', and 'blue'.) For a more complete discussion of how we get color information out of the single brightness values measured at each pixel well, please see RAW files store 3 colors per pixel, or only one?

_{¹ Please see: Why are my RAW images already in colour if debayering is not done yet?}

Anytime you view a "raw" image on any device with any particular viewing/editing application, one of two things is happening:

• The raw data in the file is being processed and interpreted by the application you are using to view the image. That application may be a simple photo viewer built into the device's firmware, or it may be a sophisticated photo editor such as Lightroom or Photoshop. There is no single "correct" interpretation of the data in a raw image file. Each application can interpret the raw data in the file differently. There is no "one" way to render the linear 12-14 bit monochromatic luminance values contained in a raw file in color on a 8-bit three color device. The raw data must be processed to be viewed.
• You are seeing a preview JPEG generated by the camera that took the shot. This preview image is appended to the file containing the raw image data, along with the metadata generated by the camera. Many devices will use this preview image when you open a raw image file.
• Some (many) applications will display the preview image until they can render an image created by interpreting the raw data itself. Other applications generate their own preview images when raw files are imported into that application's catalog. Many applications have user selectable options that allow the user to select what is displayed when a raw image file is first opened: the jpeg preview or one of many possible interpretations of the raw data using an automated routine or one of many selectable default processing profiles.

Now, back to this part of your question:

If I choose to edit the DNG in a non-Adobe application such as Luminar / Dark Table or another, e.g. Shotkit, then will the DNG images open as if the photographer had made no edits (i.e. in RAW original) or would they open with the edits applied?

What you will see on your screen when they first open depends upon:

• How the DNG was created/copied and what is the source of the JPEG preview embedded within it. It's highly possible the original JPEG preview embedded in the raw file at the time the camera took the photo is still in there and will be the first thing you see. It's also possible when the original raw file was converted to DNG the preview image was replaced with another preview image created by the implementation that did the conversion to DNG. Without knowing what application was used to convert to DNG it's hard to say. Depending upon how your client's import settings were configured when they imported the raw files, you may see a preview image generated by LR and appended to the raw file upon that import by your client.
• How the application you are using to open the DNG file is set display the image when initially opened. Does it initially display the embedded preview JPEG? Does it display a preview generated when you imported the image(s) to the application you're using to open them? Does it display the JPEG preview while it is crunching the numbers, then switch to a display of it's own interpretation of the raw sensor output based on an automated routine or one of many selectable default processing profiles?

Related questions:

RAW files store 3 colors per pixel, or only one?
Why is there a loss of quality from camera to computer screen
Why do my photos look different in Photoshop/Lightroom vs Canon EOS utility/in camera?